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Abstract. Atmospheric inverse modeling describes the process of estimating greenhouse gas fluxes or air pollution emissions at the Earth's surface using observations of these gases collected in the atmosphere. The launch of new satellites, the expansion of surface observation networks, and a desire for more detailed maps of surface fluxes have yielded numerous computational and statistical challenges for standard inverse modeling frameworks that were often originally designed with much smaller data sets in mind. In this article, we discuss computationally efficient methods for large-scale atmospheric inverse modeling and focus on addressing some of the main computational and practical challenges. We develop generalized hybrid projection methods, which are iterative methods for solving large-scale inverse problems, and specifically we focus on the case of estimating surface fluxes. These algorithms confer several advantages. They are efficient, in part because they converge quickly, they exploit efficient matrix–vector multiplications, and they do not require inversion of any matrices. These methods are also robust because they can accurately reconstruct surface fluxes, they are automatic since regularization or covariance matrix parameters and stopping criteria can be determined as part of the iterative algorithm, and they are flexible because they can be paired with many different types of atmospheric models. We demonstrate the benefits of generalized hybrid methods with a case study from NASA's Orbiting Carbon Observatory 2 (OCO-2) satellite. We then address the more challenging problem of solving the inverse model when the mean of the surface fluxes is not known a priori; we do so by reformulating the problem, thereby extending the applicability of hybrid projection methods to include hierarchical priors. We further show that by exploiting mathematical relations provided by the generalized hybrid method, we can efficiently calculate an approximate posterior variance, thereby providing uncertainty information.
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Geostatistical inverse modeling with very large datasets: an example from the Orbiting Carbon Observatory 2 (OCO-2) satellite
Abstract. Geostatistical inverse modeling (GIM) has become a common approach to estimating greenhouse gas fluxes at the Earth's surface using atmospheric observations. GIMs are unique relative to other commonly used approaches because they do not require a single emissions inventory or a bottom–up model to serve as an initial guess of the fluxes. Instead, a modeler can incorporate a wide range of environmental, economic, and/or land use data to estimate the fluxes. Traditionally, GIMs have been paired with in situ observations that number in the thousands or tens of thousands. However, the number of available atmospheric greenhouse gas observations has been increasing enormously as the number of satellites, airborne measurement campaigns, and in situ monitoring stations continues to increase. This era of prolific greenhouse gas observations presents computational and statistical challenges for inverse modeling frameworks that have traditionally been paired with a limited number of in situ monitoring sites. In this article, we discuss the challenges of estimating greenhouse gas fluxes using large atmospheric datasets with a particular focus on GIMs. We subsequently discuss several strategies for estimating the fluxes and quantifying uncertainties, strategies that are adapted from hydrology, applied math, or other academic fields and are compatible with a wide variety of atmospheric models. We further evaluate the accuracy and computational burden of each strategy using a synthetic CO2 case study based upon NASA's Orbiting Carbon Observatory 2 (OCO-2) satellite. Specifically, we simultaneously estimate a full year of 3-hourly CO2 fluxes across North America in one case study – a total of 9.4×106 unknown fluxes using 9.9×104 synthetic observations. The strategies discussed here provide accurate estimates of CO2 fluxes that are comparable to fluxes calculated directly or analytically. We are also able to approximate posterior uncertainties in the fluxes, but these approximations are, typically, an over- or underestimate depending upon the strategy employed and the degree of approximation required to make the calculations manageable.
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- Award ID(s):
- 1720398
- PAR ID:
- 10165258
- Date Published:
- Journal Name:
- Geoscientific Model Development
- Volume:
- 13
- Issue:
- 3
- ISSN:
- 1991-9603
- Page Range / eLocation ID:
- 1771 to 1785
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.5194/gmd-13-1771-2020
